We consider two-dimensional Schrödinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve composed of a circular arc and two straight semi-lines. Using a test-function argument with help of parallel coordinates outside the cut-locus of the curve, we establish the existence of discrete eigenvalues. This is a special variant of a recent result of Exner (2020 J. Phys. A: Math. Theor.
53 355302) in a non-smooth case and via a different technique which does not require non-positive constraining potentials.